SOLUTION: Slove for X http://postimg.org/image/kuutoilsl/dbd4001e/ Geometric Mean

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Question 1011802: Slove for X
http://postimg.org/image/kuutoilsl/dbd4001e/
Geometric Mean
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

altitude divides triangle into two right triangles which are similar
so, their side are proportional
hypothenuse of the original triangle is divided by altitude into part that is long and part that is long; so, the length of hypothenuse is
and the length of the leg is
so we have proportion:







Answer by ikleyn(52909)   (Show Source): You can put this solution on YOUR website!
.
In a right-angled triangle the altitude drawn to the hypotenuse, is geometric mean of the segments it divides the hypotenuse.

It means that the altitude drawn to the hypotenuse has the measure  =  = 4.

Now consider the smallest triangle. You know its legs.
They are 4 units and 2 units long.

Hence, x =  =  =  = .

The problem is solved.


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